Corollary 4.7.3.9. Let $\lambda $ be an infinite cardinal and let $\kappa = \mathrm{cf}(\lambda )$ be its cofinality. Suppose we are given a collection of $\lambda $-small sets $\{ T_{s} \} _{s \in S}$. If the index set $S$ is $\kappa $-small, then coproduct ${\coprod }_{s \in S} T_ s$ is $\lambda $-small.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$